I have the question y=-|x^2 -9|

Question

I am asked for the piecewise function. I have written
y={-x^2 +9 if x less than equal to -3}
{ x^2 -9 if x is greater than equal to 3}
I am wondering if I have my are signs backwards.My reasons for choosing the signs I have is if I plug a negative number into the first one and square it, it will be positive and then the negative out front will make it negative. Is there a trick to getting the signs right?

Answer 1

Not only are the signs backwards, but the intervals are incorrect as well.

Take a look at the graph and see whether you can fix it.

http://www.wolframalpha.com/input/?i=-|x^2-9|+for+-5+%3C%3D+x+%3C%3D+5

The trick to getting signs right is remembering that

|x| = x if x >= 0
|x| = -x if x < 0